Hi all,

I want to prove the following algebraically (that is, NOT with calculus): If an object with initial velocity

is accelerated at some constant acceleration over a time

, and finishes with a final velocity of

, then the average velocity of the object is

. This average velocity is the equivalent velocity that this object would have to be travelling (without acceleration) to travel the same distance as the object experiencing acceleration as above.

I need to somehow prove this in order to derive the kinematic equations. But how? It is easy to derive the kinematic equations with a knowledge of calculus, but if you are teaching this to someone without a knowledge of calculus, how can this be proven rigorously?